Periodic spin unrestricted DFT-PW91+U calculations together with ab initio thermodynamic modeling were used to study the structure, defects, and stability of different terminations of the (100) surface of cobalt spinel under various redox conditions imposed by different oxygen partial pressure and temperature. Three terminations containing under-stoichiometric (100)-O, stoichiometric (100)-S, and overstoichiometric (100)-R amount of cobalt ions were analyzed, and their atomic and defect structure, reconstruction, and stability were elucidated. For the most stable (100)-S and (100)-O facets, formation of cationic and anionic vacancies was examined, and a surface redox state diagram of possible spinel (100) terminations in the stoichiometry range from Co 2.75 O 4 to Co 3 O 3.75 was constructed and discussed in detail. The results revealed that the bare (100)-S surface is the most stable at temperatures and pressures of typical catalytic processes (T ∼ 200°C to ∼500°C, p O2 /p°∼ 0.001 to ∼1). In more reducing conditions (T > 600°C and p O2 /p°< 0.0001), the (100)-S facet is readily reduced by formation of oxygen vacancies, whereas in the oxidizing conditions (T < 200°C and p O2 /p°> 10), coexistence of (100)-S and (100)-O terminations was revealed. Formation of the oxygen vacancies involves reduction of the octahedral trivalent cobalt and is accompanied by migration of the divalent tetrahedral cobalt into empty, interstitial octahedral positions. It was also found that the constituent octahedral Co cation proximal to the interstitial cobalt adopts a low spin configuration in contrast to the distal one that preserves its surface high spin state. In the case of the Co depleted surfaces, the octahedral vacancies are thermodynamically disfavored with respect to the tetrahedral ones in the whole range of the examined T and p O2 values. The obtained theoretical results, supported by TPD-O 2 and TG experiments, show that the octahedral cobalt ions are directly involved in the redox processes of Co 3 O 4 .

In this paper we present a theoretical study of water sorption on cobalt spinel nanocrystals by means of plane-wave periodic density functional theory (DFT) calculations jointly with statistical thermodynamics. The three most stable (100), (110), and (111) planes exposed by Co 3 O 4 were considered, and their stabilization upon water adsorption is discussed in detail. The calculated changes in free enthalpy of the investigated system under different hydration conditions along with the Wulff construction were used to predict the rhombicuboctahedral equilibrium morphology of cobalt spinel nanocrystals in different conditions, which corresponds very well to the experimental transmission electron microscopic (TEM) images. Two-dimensional surface coverage versus temperature and pressure diagrams were constructed for each of the examined (100), (110), and (111) planes to illustrate water adsorption processes in a concise way.

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Periodic spin unrestricted, gradient corrected DFT calculations joined with atomistic thermodynamic modeling and experiment were used to study the structure and stability of various reactive oxygen species (ROS) and oxygen vacancies produced on the most stable terminations of the cobalt spinel ( 100) surface. The surface state diagram of oxygen in a wide range of pressures and temperatures was constructed for coverage varying from Θ O = 1.51 atom•nm −2 to Θ O = 6.04 atom•nm −2 . A large variety of the unraveled surface ROS includes diatomic superoxo (Co O −O 2 − −Co O ), peroxo (Co T −O 2 2− −Co O ), and spin paired (Co O −O 2 −Co O ) adducts along with monatomic metal-oxo (Co T −O + , Co O −O 2+ ) species, where Co T and Co O stand for the tetrahedral and octahedral cobalt surface centers, respectively. There are also two kinds of peroxo species associated with surface oxygen ions connected with 3Co O or 2Co O and 1Co T cations ((O 2O,1T −O) 2− and (O 3O −O) 2− ), respectively). The results revealed that in the oxygen pressure range of typical catalytic reactions (p O 2 /p°from ∼0.01 to 1), the most stable stoichiometric (100)-S surface accommodates the Co T −O 2 2− −Co O and Co O −O 2 −Co O adducts at temperatures below 250−300 °C. In the temperature from 250 to 300 °C and from 550 to 700 °C, it is covered by the O species associated with the exposed tetrahedral cobalt sites (Co T − O + ) or remains in a bare state. In more reducing conditions (T > 550−700 °C), the (100)-S facet is readily defected due to trigonal oxygen (O 2O,1T ) release and formation of surface oxygen vacancies. The reactivity of surface ROS was tested in 16 O 2 / 18 O 2 isotopic exchange, N 2 O decomposition, and oxidation of CH 4 and CO model reactions, carried over Co 3 O 4 and Co 3 18 O 4 nanocrystalline samples with the predominant (100) faceting revealed by high angle angular dark field STEM examination. The Co O −O 2+ adducts associated with octahedral cobalt sites, as well as the peroxo (O 2O,1T −O) 2− and (O 3O −O) 2− surface species being thermodynamically unstable are involved in surface oxygen recombination processes, probed by 16 O 2 / 18 O 2 exchange and N 2 O decomposition. It was shown that at low temperatures CO is oxidized by the suprafacial Co O −O 2 −Co O and Co T −O 2 −Co O diatomic oxygen, whereas in CH 4 activation, the highly reactive cobalt-oxo species (Co T −O + ) are involved. Above 600 °C at p O 2 /p°= 0.01, due to the onset of oxygen vacancy formation, the suprafacial methane oxidation gradually changes into the intrafacial Mars-van Krevelen scheme. The constructed surface phase diagram was used for rationalization of the obtained catalytic data, allowing delineation of the specific role of the chemical state of the cobalt spinel surface in the investigated processes, as well as the range of the corresponding temperatures and oxygen pressures. It also provides a convenient background for molecular understanding of remarkable activity of Co 3 O 4 in many other catalytic redox reactions.